Teaching Stats in High School

An interesting thread came across my twitter feed, posted by the wonderful author Steven Strogatz. It was especially timely as I am hoping to find a way to add a Statistics class to our program here at Mid-Pen (while also hoping to reduce my classload from 6 to 5 classes – talk about needing a mathemagician! Anyone know a great math teacher who wants to teach 2 classes for free?) And it brought up an argument that I’ve thought a lot about over the last couple of decades.

I didn’t take statistics in high school. It wasn’t offered at my school at the time. When I entered Bates College, my first semester, one of the classes I enrolled in was BIO 244, an introductory class in Biostatistics. This was a long time ago, but I don’t remember being impressed by the class. I remember entering data into MATLAB, following recipes for statistical tests, and not feeling like it made a lot of sense. To be honest, I was also a very young first semester college student and probably didn’t take my academics as seriously as I should have. (Mind you, that had been true throughout middle and high school, and would continue through college. I finally learned how to be a student in grad school, but that’s another topic.)

MATLAB has come a long way since the 1990’s console window version!

My next exposure to statistics was MATH 215, a pure statistics class that had pre-requisites of MATH 206 (Multivariable Calculus) and MATH 214 (Probability). Here it was – the rich and theory based statistics that let you get your hands dirty with integrals and proofs and all the stuff that those non-math people couldn’t understand (or so I thought at the time, from my isolated and prestigious tower I imagined myself living in). Now this was the statistics class that I was looking for – nothing about data interpretation, except from a pure mathematical standpoint.

Finally, in my senior year in college, I decided to take a nice, easy class – and what do you know? There was PSYC 218, a statistics class in the Psychology Department. I figured it’d be an easy A – and if it was just about the math, I would have been right. In fact, I was that annoying student who had to show the professor that I knew the math better than he did, pointing out errors in the explanations of various tests and why they worked. I was also the student that lots of people came to in class when they didn’t get how to do the math. Unfortunately for me, there was a lot more in that class about how to design experiments, evaluate experiments, make conclusions based on the data, interpret results, and lots of other things that just didn’t seem to matter to me because they weren’t about the pure math. And (at the time) I was only about pure math. Applied math was a pointless waste for people who couldn’t live in my world of number theory and topology and elliptical curves.

Fast forward a few years, and I found myself teaching, which meant making the math relate to the real world for students, to make it meaningful and relevant. I was the only math teacher in a tiny high school program of 19 students, and was teaching Pre-Algebra, Algebra 1, Geometry, and Algebra 2…and U.S. History. (We had a math, science, and English teacher, and each of us had to take on a social studies class until the program grew.)

And grow it did…more than doubling in size over the next seven years that I was there. I started teaching calculus, and eventually was talked into teaching A.P. Statistics. And I was really wary of this – it didn’t require calculus, and how could you teach statistics without calculus? I had seen it go poorly1 for both biology and psychology classes at a very prestigious small college. But I decided to give it a try, and it worked well for students. A few years later, at a different school, I offered the same class, with some excellent results from students. And I realized that Statistics fits an important niche in the math education curriculum. It is a class that is taught exclusively as an applied course, which is different from how we teach Algebra and Geometry and Calculus. For those classes, even if we focus on how they can apply to the real world, that never seems to be our primary focus. And that’s okay I think. But statistics opens up the world of how to interpret data, whether in the sciences or social sciences. It’s power gives it validity and usefulness to many students I’ve had who, even when they come around to thinking that logarithms are cool and the Law of Cosines in vector form is amazing, have not experienced in other classes.

So, back to that thread in the beginning. Twenty-five years ago, I would have been firmly in the camp that calculus is required for statistics. And it’s true that knowing calculus may be required for understanding the theory of statistics. But a high school or introductory statistics class should be about how to use statistics, how to apply and interpret statistical tests, how to evaluate the use of statistics (especially in this era of fake news).

Florence Nightingale’s Coxcombs led to great advances in epidemiology.

It also offers some great historical stories about the development of statistics, and gives the opportunity to talk about Florence Nightingale’s contributions during the Crimean War.

Statistics can be a great class for the math student who has already taken calculus, and they can be encouraged and guided through some of the theory behind statistics. It can also be the perfect class for the student who is sure they are not going on in math or science but has finished Algebra 2 and wants a math class on their transcript. Make no mistake – I’m not calling this a math class for non-math people. What I am calling it is a chance for students to make a choice to take a math class that they see as relevant, that they will buy into, that they won’t question when they’ll use it because it is clear in every lesson just how it can be used. In the end, doesn’t this give them a greater appreciation for the richness of math?


1In retrospect, it is clear that my memories of those classes were colored by my biases about math as well as my poor student skills – they may have been outstanding classes, after all.

Working on Feminism in Math Class

My college adviser in math, Professor Bonnie Shulman, has been one of my biggest influences in my math education career. She inspired me as a teacher who could help s35dd7datudents find the excitement and joy that mathematics could bring them. I had entered Bates as a relatively young first year student, definitely over-confident, and with no real idea for what I would do with my life – probably become a doctor since I liked the idea of helping people, and it seemed like it would be a nice challenge. After my first semester, I realized that I really didn’t like chemistry and there would be a lot of chem required for pre-med, it would be hard for me to not major in music after having devoted so much of my life to writing and performing in various ensembles, and most significantly, that math wasn’t just easy for me – it was actually a lot more interesting and fun than I ever gave it credit.

Much of Bonnie’s focus was how to get more girls and women involved in math and science. As I started my teaching career, I made a conscious decision to give all of the girls in my math classes the most encouragement, the highest expectations, and the best future in STEM careers. And I failed miserably. Well, maybe not miserably, but I didn’t have them leaving my class and going straight into prestigious colleges and universities and graduating with math and science degrees. And I was sure the problem wasn’t me, because you know what I found? None of my female students had confidence. At least, that’s what I saw. When I asked a question in class, they didn’t raise their hand. If I called on them anyway, they would mumble, or say they didn’t know. If they did answer, they did so in a questioning voice. And what would I tell them? “Speak up! Speak confidently! Don’t answer with a tone that keeps going up!” And that fixed none of the problems. That is, maybe they would answer in that moment with a louder and less questioning tone, but their lack of confidence hadn’t really changed.

This isn’t to say that there weren’t issues of confidence that these girls had learned over the previous 8, 9, 10, or 11 years of classes before they got to me. And yet, despite my best intentions, all I was doing was pointing out their lack of confidence. Any progress that they were making in improved confidence was incremental, and probably being undone by my pointing out how they weren’t being enough like the male students.

I don’t pretend that I have all the answers now. I still have high expectations for my students, regardless of gender (male, female, trans, non-binary, fluid), and I make every effort to let each student know that I believe in them. But I don’t call on students when they aren’t volunteering. I don’t demand that they answer with confidence. In fact, I now relish the questioning, since doubt allows us to develop deeper and more interesting explorations into the mathematics. And with more time for reflection, I’m sure that I could figure out other things that I do that help.

One thing I do know is that I am surrounded by Dr. Johanna Nelson at SLAC's SSRL synchrotron facilityamazing girls and women in my life, many of whom absolutely love and appreciate math and science (including a large number of my previous students). I am also grateful for having my wife in my life, for many other reasons of course, but for the purpose of this post, because I find myself talking about a woman who is a successful physicist on probably a weekly basis in my classes.

Now, sixteen years after having started my teaching career, I have two (very different) young daughters, and a whole new lens to look through when I think about how I approach my teaching style for my non-male students, and also for my male students. I want to encourage all of the positive behaviors that students can have, regardless of their gender and regardless of gender stereotypes. I also want to remember to meet each student where they are, and to do everything I can to help them see the exciting things that math can tell us about the world and ourselves. Or sometimes, show them how we can just have fun with math.

Extra Credit? No More!

I used to give out extra credit. Not just at the beginning of my career, but right up through last year. I just thought it’s something that teachers do, even though I knew better, and even though it never really accomplished what I wanted it to accomplish. So finally, this year, I told my students that I was done. Those awesome challenge problems? No longer for extra credit. Attending a Stanford Public Math Lecture? No more extra credit for that. Predictably, students told me how unfair this was, how stupid this was, what could I be thinking?

Inspired by a tweet (shown above) by Brad Weinstein, I decided it was long past time to blog about this decision to tell others exactly what I told my students. So here it is…

What do we, as teachers, give extra credit for? To reward students for awesome and interesting things that they do that may not directly be a part of what we are normally grading them on. In other words, we are bringing up a student’s grade, not because they understand the thing that the class is all about, but because they did something outside of the class expectations. And if you have spent time in a classroom with extra credit, perhaps you’ve seen what I’ve seen. The students who do the extra credit tend to fall into one of two categories:

  • High achieving students who wants to bring their 99% up to 100% (because they are hypercompetitive or tie their own self worth to their grade).
  • Students who have not been doing classwork or homework and now realize that their D+ will get them in trouble with their parents and they want an easy way to at least get a C-.

So what is the result when a student does a ton of extra credit to bring their grade up by 3, 5, even 10 or 15 points? Their report card becomes a lie – or at least misrepresents their accomplishements. In theory, to me, a student who receives a C in, say, a Geometry class is a student who has demonstrated that they have a moderate understanding of the material presented, who may have never successfully and independently completed a proof but who gets the basic relationships between different shapes and figures, who has some grasp of parallel lines, congruent triangles, and how to find areas from formulas (even if they don’t memorize much and retain much in the way of details afterward). The main takeaway is that the student should have reached a certain conceptual understanding of geometry and spatial mathematics that will be useful in future math classes.

But what happens with a student who had a D, extra credit brings them up to a C, and certain assumptions are made about their conceptual understanding of geometry. This does them a disservice when they go to future classes, when their Algebra 2 or PreCalculus teacher get an invalid impression of their skillset in Geometry. This kind of grade inflation drives teachers crazy as well.

And what is it that we want students to get out of these extra credit assignments, anyway? The fascination and joy that can be found in mathematics, and the beauty, creativity, and surprises that arise in a really interesting problem. I want my students to get that, make no mistake, and I can incorporate a lot of that into my classes. When something comes up that doesn’t directly apply to a class, I can still bring it to my students because it is absolutely worthwhile for them to be exposed to all of this rich mathematics that doesn’t show up in a syllabus or in a typical high school textbook. Plus, when students see me get really excited about a math problem, it gets them excited, and that happens a whole lot more when investigating graph theory or topology than when solving linear systems by graphing or entering data into a table in my calculator to find a logistic regression function.

Plus, I want to reward students for their contributions to a positive math culture, especially by taking risks, by sharing their mistakes, by (respectfully and kindly) pointing out mistakes of others (including/especially me), by working well as a team, by helping their peers, and by bringing to class math that they find in the real world. So, to reward students for those contributions to our math world without artifically inflating their grades, I offer students points. To a degree they are subjective, which means that at times I will give a well meaning student the benefit of the doubt. It won’t affect their grade, just their current point total.

I announced at the beginning of the year that there will be individual prizes for the students with the most points at the end of the semester, and a class prize for the class whose students have as a whole earned the most points (representing a very positive math culture in a class). While there are some students who still grumble about not having extra credit anymore, many students are fairly invested in the idea of extra points. The semester ends this coming Friday, we have finals next week, and the following week, students will receive their prizes. The class prize will probably be a lunch – something simple, anyway, and food is always popular. The individual students will come with me to attend a showing of Hidden Figures.


One of the first big opportunities for students to receive extra points next month will be by attending the Stanford Public Math Lecture by Ingrid Daubechies on Mathematicians, Art Historians, and Conservators. These public lectures are a real treat, and often very accessible to high school students. The best part is, whether through a movie or a public lecture, students get a chance to learn more about, and be inspired by, real mathematicians. Isn’t that worth more than all the extra credit in the world?


Rethinking Vocabulary

In math, vocabulary is important. I mean, it’s really, really important. It’s important to those of us who can’t stand when someone points at an equilateral rectangle and a non-equilateral rectangle and insists the equilateral rectangle can ONLY be called a square, and it isn’t a rectangle. It’s important to those of us who know that the word unique doesn’t just mean unusual. Then we develop tons of notation and jargon, and we speak in our own funny language, and tell students that if they want to join the math party, they have to memorize all of these obscure words with different meanings than they’ve been taught before.

This has always been problematic to me, and I think I have a better idea of why now. As with so many revelations, this was largely born through thinking about Dan Meyer’s analogy of a problem being a headache, and math being the cure. But…these are always about the problem that a student is trying to solve without knowing the math required, and creating that need in the student to learn the math for a better reason than because we say so.

Well, what if we taught math vocabulary that way? That is, instead of telling students that the side opposite the right angle in a right triangle on a plane is called a hypotenuse, let them realize that it’s pretty tedious to always refer to the side opposite the right angle in a right triangle on a plane as the side opposite the right angle in a right triangle on a plane.

Polygraphs in Desmos I think are a great way to develop this need, where the vocabulary is the cure. I make a point in my class of how important it is to be precise in your mathematical communication, and I never test students on vocabulary. However, I make a point to use the relevant vocabulary regularly once we’ve defined it in the class. I also don’t take off credit if a student does not use the most efficient vocabulary. If she really wants to say the side opposite the right angle in a right triangle on a plane instead of hypotenuse, that’s up to her. As long as she is communicating her ideas effectively, eventually she will recognize the need to be more efficient. Generally, I don’t find that students in my class struggle with vocabulary even though I don’t test them. Both verbally and in written form, that just isn’t a common stumbling block.

My goal now is how to put more thought into making the extraneous words and extra writing and speaking enough of a headache that students are asking for vocabulary words to simplify our language. Does anyone out there do something like this – intentionally? Curious for those who do word walls – what’s your approach? Student created? Definitions/diagrams included? How much do you find it helps? Could the word walls become an aspirin for our challenging language?

Why Prove Things? A Geometry Debate

Earlier this week, my geometry students took part in a new debate format. As is often the case, the topic was student generated. Every year, students inevitably complain about proofs in geometry. It generally happens based on what they have heard from parents  or older friends who have horror stories about their experiences with impossible wastes if time, and it comes up before we do proofs. Once we start doing proofs, students question why we are proving things that were already proven. “Shouldn’t geometry be about measuring angles and lengths and areas and volumes?”, they ask. “Why can’t we just apply what others have proven before us? What’s the point?”

Of course, I have my reasons, but  

Pythagorean Triples For The Whole Class!

After introducing my geometry students to the Pythagorean Theorem, I introduced them to the idea of Pythagorean Triples. I showed them that the numbers 3, 4, and 5 will work in the equation: 32+42=52. Then I had students pick a couple of numbers, and we generated a brand new Pythagorean Triple with some fun algebra. At least, I thought it was fun, and students were curious where I was going with my algebraic manipulations. There are several methods, but the one I used went like this.

Pick two interesting numbers. Make them integers, not too big, but not too small. Did I hear 7 and 19? Perfect.

First, multiply those two numbers, and double your answer:
2 ∙ 7 ∙ 19 = 266

Next, find the (absolute value of the) difference of the squares of those two numbers:

192 – 72 = 312

Now, find the sum of the squares of those two numbers:

192 + 72 = 410

And just like that, we have a brand new Pythagorean triple:

2662 + 3122 = 4102

Go ahead – check it on your calculator if you’d like. Pretty nice, huh? I’ll leave it to you to do the algebra to see that it will always work. The most amazing thing about this little task is that students were immediately convinced (and rightly so) that even though it may be hard to find Pythagorean triples, there are an infinite number of them.

And then the game started. I gave each group of 3-4 students a stack of 24 numbers that can be turned into 8 sets of Pythagorean triples. (Of course, there’s only one way to get all 8 sets, but since there are some doubles, it’s possible to match up some that will throw you off).

For both of my geometry classes, all students (no exaggeration!) were engaged bell to bell, furiously testing and playing with the numbers, discussing strategies, and trying to find the eight correct sets. Not only that, although students were in separate groups, they soon realized that they’d be more successful working together. I heard so many great ideas about how to attack the problem that I wasn’t surprised when, even though it came down to the wire, one of the classes found all 8 sets!

This, to me, was a great low floor, high ceiling activity. Every student was able to work on calculations – calculating squares, calculating sums, etc. And some students really worked through some great strategies – what units digits can sum to the biggest number’s units digit? Can we work backwards from that? And of course, the little bit of algebra review in the beginning was helpful as I found later, when I had students repeat the process to develop their own new Pythagorean triples. It was easy for them to check their answers at the end and then look for any mistakes they may have made, and there’s something about big numbers that makes students truly proud (and rightfully so, even when they are using a calculator to do the calculating work).

Student Generated Problems Are Best!

Around this time of my geometry course each year, students have learned a whole lot of geometry – parallel lines, congruent triangles, basic proof techniques. It is the perfect time for them to come up with challenge problems for me. Believe it or not, classes never disappoint in this fashion. I’ve had some great questions in the past. (One of my favorites – can you fold an 8.5 by 11 piece of paper into an isosceles triangle where the entire triangle has the same number of layers of paper. I’m still not sure about that one, but I really enjoy watching students try every year.)

I tell my students that there are two things that make a challenge problem great:

  1. It is relatively easy to explain to anyone.
  2. It is challenging to find a solution (or even figure out if a solution is possible).

This year, a student came up with a problem that fit those requirements perfectly: Is it possible to take a square, and cut it into isosceles triangles that aren’t congruent? We then restated it to require a finite number of non-isosceles triangles (though the fractal version is a pretty cool visual and a nice approach).

We spent a few minutes on this at the end of class, but didn’t get anywhere right away. I sent this out via twitter, and almost immediately got a tweet back from Henri Picciotto:

What? That brought out some resolve in me to find a solution, and later that day I did. The next morning, before school, I had a student rush in to show me her solution, which was pretty similar to mine. I suggested to both my geometry classes that there may be more solutions – how many unique solutions or approaches may there be? Can we find an even number? Fewer than seven? I ended up waking up in the middle of the night thinking about this, and came up with even more solutions. So far, I’ve got solutions for 6, 7, 8, 11, 13, and 17 triangles. But the best part of this whole story is that a week later, I have students talking about this before and after school, at lunch, outside my classroom, totally invested in a problem that they made on their own.


When you are a teacher, these are the moments that you live for. Students of varying backgrounds and supposedly different ability levels collaborating and arguing with passion about squares and triangles. Sometimes, that question of “When am I going to use this?” or “How does this apply in the real world?” never come up because the math, by itself, is just fun.

So…can anyone find a solution with fewer than 6 triangles?

Reflections on a Busy Year

Yes, I’ve been busy before, and yes, all teachers are perennially busy, but this year has been different. The summer before the school year, I was asked to teach a second section of Algebra 1. The enrollment at our school increased (yay!) but not enough to hire another math teacher (boo!). I agreed, and am receiving a nice stipend to do it (which we’re pretending we don’t have and putting straight into savings). What I wasn’t prepared for was just how little time I would have. Teaching six periods, with no prep period at school, and spending most of my time before school, during lunch, and after school working with students has left me no time during the school day to do those other parts of my job that are important (if sometimes menial) – reviewing lessons from years past, preparing and updating lessons, reflecting on daily lessons, communications with parents, and oh so much grading and student feedback. I had a schedule like this in the past, but there were a few things that were very different.

  1. I was much younger, and had much more energy.
  2. My commute was much shorter (15 minutes vs. 45-75 minutes).
  3. I didn’t have any kids at the time. Man, having kids really eats up your time. Making breakfast, giving baths, story time, preparing lunches, putting the girls to bed. (Make no mistake about it – my wife does as much as I do, sometimes more, but we do try to split the duties evenly).
  4. I decided to implement standards based grading (which I really need to blog about), an endeavor that is mostly working really well, but needs some tweaks to push forward.
  5. For my Algebra 1 class, I finally decided to move forward with CPM, which has meant a lot of extra work and a very different approach to my teaching style.

I fully chose to do this, but it’s led to working from 8 to 11 or later most nights, while waking up at 5:30 every morning, working most of the time on weekends, mostly not blogging this semester, and committing to myself to not do this to myself again. I ‘m well past the point of being in danger of burning out (I think) in this career, but next year I want some more time for myself and my family, and maybe really think about doing that Desmos fellowship that I decided not to apply for this year (but instead followed longingly on Twitter).

So, for all you teachers in a similar position, I’d love to know what strategies you have. What do you cut back on? What do you just cut out? How do you survive? Any thoughts on how to be productive during commutes besides listening to podcasts, etc.?

Also, if you are interested, blog posts should be coming, in no particular order, on:

  • Some Thoughts on Implementing Standards Based Grading (So Far)
  • Debate #2: Discrete vs. Continuous Graphs
  • Debate #3: Do We Need to Prove Things in Class That People Already Proved?
  • A Great Geometry Question from a Student
  • When a Pythagorean Triples Warm-up Becomes a Class Long Activity

I’ve got a nice long train ride from LA to San Jose after Thanksgiving, and maybe after finishing my Asilomar Talk (11:00, Oak Shelter – Get Your Students Talking: Introducing Debate to Math Class, with Noirin Foy), sub plans, and grading, I’ll put some thoughts down. Thankfully, the in-laws will be coming with us on the train, and should occupy the girls while my wife and I get some valuable time to work.

Show, Don’t Tell!

For much of the early part of my teaching career, there was a strong focus on literacy from “the outside”. In other words, as soon as I stepped out of my own math classroom, I was bombarded with messages of how important it was to build literacy in students, and how the primary goals in schools needed to be about literacy above and beyond all other topics. To be fair, I started my teaching career at a school for students with various learning differences, but which at that time had a strong focus on dyslexia and other literacy-based disabilities. I am sure that had an impact on the messages I heard, from parents, from administrators, and from the speakers we had and conferences we attended during professional development. Still, there seemed to be a focus on literacy at the expense of math. As a beginning teacher and still in my mid 20’s, I took much of that message personally, and found myself both explicitly and implicitly arguing in favor of the need for more focus on math, which I saw as “the great equalizer” (as described by Edward James Olmos’ portrayal of Jaime Escalante in Stand and Deliver). 

Now, 16 years later, and in my very, very late 20’s, I have come to see math take center stage in prominence, thanks, for better or for worse, to Common Core. It has been literature refreshing to become more aware of the education world outside of math education, and see that we math teachers have a pretty prominent position in shaping (or trying to shape) the conversation about what education should mean in the 21st century. Thanks in part to Robert Kaplinsky’s #ObserveMe movement, I was reminded that I can learn a lot from every teacher, and at a small school like mine with a math department of 3, learning from teachers in other departments is almost an expectation.

Enter Laurie Miller, a veteran literature tLaurie Millereacher who led a small workshop during our inservice at the beginning of the year on the idea of “Show, Don’t Tell”. I’ve definitely heard the terminology before, but never spent any significant time on it that I remember in any of my English classes. We went through a nice activity where we read a passage and attempted to identify when the author was showing and when the author was telling. In the rich discussion afterwards, I found myself wishing we had more time to explore this idea, but also wondered when I would really use it (except in the written projects that I have my students do throughout the year).

A couple of weeks later, our other math teacher noted that she used the terminology to encourage a student to show their work, and things started to click. Asking students to show me their work in the past often went nowhere, because they had given the answer, and if the answer was right, why does the work matter? That can be a difficult argument to win as a teacher without resorting to authoritarian tones. But this new, simple phrase, one that students were buying into because they hear it in every class, really says it all. “Tell” is “give me the answer”, and that lends itself to a closed conversation of right or wrong. “Show”is along the lines of “convince me” or “prove it”, and leads to an open conversation about methods, efficiency, effectiveness, clarity, cohesion, organization, persistence, and all the stuff that we think of as important, and as transferable outside of our math class bubble.

I realize that this is a hastily written blog post, poorly edited, and probably rife with “tell, don’t show” examples, but in my defense, implementing SBG in Geometry and Pre-Calculus, switching to CPM for Algebra 1, and having 6 classes and no prep periods, plus a 2 year old and 5 year old at home, lead to lots of late night grading and very little time for blogging so far this year. And that’s unfortunate, because between SBG, CPM, and math debates, I have so many things to write about…over Thanksgiving break? Winter break? Hopefully sooner? Time will show.



Day 1 Debate: What Number is Best?

I know there’s a tendency to spend the first day of class talking about rules and expectations and grading policies and the syllabus and lots of other stuff that bores kids silly because, well, it’s boring. I mean, I know it’s all necessary for them to be familiar with, but do we really need to spend the first day doing that? It’s taken some time, but I’ve (mostly) changed to jumping right into something math related. Maybe it’s not a deep subject that we explore, but something to get students talking, and having fun, in class.

For my first day of Pre-Calculus, we didn’t hand out textbooks, we didn’t review the content standards, we didn’t sign out graphing calculators. Instead, the students fought. And laughed. And fought. And laughed. And laughed some more. Students entered the class and were told to think about their favorite number. (If they didn’t have a favorite, they were to make one up, and if they couldn’t, I’d give them one. Luckily, every student came up with one on their own.) I then told them to do some thinking, and come up with as many reasons why their chosen number was the best. Reasons could be from math of course, but also from pop culture, sports, numerology, other cultures, anthropology, mythology, religion, art, design, or whatever they chose. After five minutes of brainstorming, they discussed within their group of three or four which of their numbers was actually the best one. They then did further research for about fifteen minutes, using the Internet as a resource, to prepare arguments for why their own group’s number was awesome and the other groups’ numbers were boring. In the middle of their research time, I told students the story of the Hardy-Ramanujan number as well as the Interesting Number Paradox to give some incentive and inspiration.

When research time was up, we did a round-robin debate. I started with one group, and went around the room in a circle. Each group had up to 30 seconds to present an argument either for their number or against another number. I assigned each argument a subjective score of 1 to 3, and added it to that group (or subtracted from another group if they were arguing against another group’s number). I told them I’d keep going in a circle until I got bored with their arguments, but in both classes, the students were really impressive in their research and thought processes. During their research phases, I was also able to wander and listen to what they were thinking, how they discussed the math with their peers, and how they worked in groups.

I had some interesting arguments presented, and though I don’t remember even close to all of them, these were some highlights:

  • 4 is the only number that is spelled with its own number of letters.
  • 2 is the only even prime number.
  • 13 is the sum of the squares of the first two prime numbers.
  • 11 is both the number of points on the maple leaf of the Canadian flag and the number on the Loonie (Canadian one dollar coin).
  • There are 8 “quadrants” in 3d space (split by the xyxz, and yz planes). By the way – anyone know what they are called? Not quadrants, surely, since that’s how we refer to the 4 regions of the xy plane, but I don’t know right off.

In the end, students on winning teams got 10 points each, and runner up students received 5 points each. They aren’t extra credit, mind you – I’m doing away with extra credit, but that’s another blog post. These will go towards…something to be determined.

This was a great low floor, high ceiling activity where the richness of the mathematics was unbounded, but there wasn’t a single student who felt too intimidated to take part. One day doesn’t make an entire year, but this was a really fun way to spend our first day.